Finite Group Databasebeta

← #13072230

Subgroups — #13072230

Order 1408.

952 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4341C211yesmaximal, characteristic, complemented
2C2×#66993C211yesmaximal, characteristic, complemented
3C2×#66992C211yesmaximal, characteristic, complemented
4C2×#66938C211yesmaximal, characteristic, complemented
5C11×#392C211yesmaximal, characteristic, complemented
6#10622836C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622573C211yesmaximal, characteristic, complemented
10#10622571C211yesmaximal, characteristic, complemented
11#10622570C211yesmaximal, characteristic, complemented
12#10622569C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C23×Dic11C2211yescharacteristic
26C23×Dic11C2211yescharacteristic
27C2×#4341—24no—
28C2×#4341—24no—
29C2×#4341—24no—
30C22×D44C2211yescharacteristic
31C22×C4×D11C2211yescharacteristic
32C22×Dic22C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊Dic11C2211yescharacteristic
40#66993—24no—
41#66992—24no—
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×(C2×D11)⋊C4C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×C4×Dic11C2211yescharacteristic
49C2×C4×Dic11C2211yescharacteristic
50#66938—24no—
51C11×#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C24×C11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C23×D11C2311yescharacteristic
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—22no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11D414yescomplemented
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11D414yescomplemented
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C22×Dic11C2311yescharacteristic
102C22×Dic11C2311yescharacteristic
103C22×Dic11C2311yescharacteristic
104C22×Dic11C2311yescharacteristic
105#4341—232no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—41no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22D414yescomplemented
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—41no—
118C22⋊Dic11—22no—
119C22⋊Dic11—22no—
120C22⋊Dic11—22no—
121C22⋊Dic11—41no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127Dic11⋊C4—22no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130#2431—111nomaximal, Sylow
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11C2×D412yes—
151C23×C11C2×D412yes—
152C23×C11C2411yescharacteristic
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11C2×D412yes—
167D4×C11—28no—
168D4×C11—44no—
169D4×C11—44no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11C2×D412yes—
181C2×C4×C11#4112yescomplemented
182C22⋊D11—28no—
183C22⋊D11—28no—
184C22⋊D11—44no—
185C22⋊D11—44no—
186C22⋊D11—44no—
187C22⋊D11—44no—
188C2×Dic11—28no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—28no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11C2×D412yes—
203C2×Dic11C2×D412yes—
204C2×Dic11C2×D412yes—
205C2×Dic11C2×D412yes—
206C2×Dic11C2×D412yes—
207C2×Dic11#4112yescomplemented
208D44—44no—
209C4×D11—28no—
210Dic22—28no—
211C22×#41—111no—
212C2×#127—111no—
213C2×#124—111no—
214C2×#121—111no—
215#392—111no—
216#392—111no—
217#392—111no—
218#392D1111yescharacteristic, complemented
219#391—111no—
220#390—111no—
221#386—111no—
222#386—111no—
223#386—111no—
224#386—111no—
225C4×C22⋊C4—111no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11C22×D411yescharacteristic
248C22×C11C22×D411yescharacteristic
249C22×C11C22×D411yescharacteristic
250C22×C11C2×#4111yescharacteristic
251C22×C11C2×#4111yescharacteristic
252C22×C11H(5,𝔽2)11yescharacteristic
253C22×C11H(5,𝔽2)11yescharacteristic
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—41no—
271C4×C11—41no—
272Dic11—22no—
273Dic11—22no—
274Dic11—22no—
275Dic11—41no—
276Dic11—41no—
277Dic11#12014yes—
278C2×#41—224no—
279C2×#41—224no—
280C2×#41—224no—
281C22×Q8—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4—111no—
287C22×D4—111no—
288C22×D4—111no—
289C22×D4C2×D1111yescharacteristic
290C22×D4C2×D1111yescharacteristic
291C22×D4C2×D1111yescharacteristic
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—111no—
295#127—224no—
296#124—224no—
297#121—224no—
298C2×C4⋊C4—111no—
299C2×C22⋊C4—111no—
300C2×C22⋊C4—111no—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—111no—
307C2×C22⋊C4—111no—
308C2×C22⋊C4C2×D1111yescharacteristic
309C2×C22⋊C4C2×D1111yescharacteristic
310C2×C22⋊C4C2×D1111yescharacteristic
311C2×C42—111no—
312C2×C42—111no—
313#95—111no—
314#95—111no—
315#95—111no—
316#95—111no—
317#95—111no—
318#95C2×D1111yescharacteristic
319C2×C11—42no—
320C2×C11—42no—
321C2×C11—81no—
322C2×C11C2×#12011yescharacteristic
323C2×C11#53211yescharacteristic
324C2×C11#53511yescharacteristic
325C2×C11#54611yescharacteristic
326C2×C11#54611yescharacteristic
327C2×C11#55011yescharacteristic
328C2×C11#55011yescharacteristic
329D11—42no—
330D11—81no—
331C24—111no—
332C24—111no—
333C24C22×D1111yescharacteristic
334C24C22×D1111yescharacteristic
335C24C22×D1111yescharacteristic
336#41—2232no—
337C2×Q8—114no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—114no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—441no—
370C22×C4—111no—
371C22×C4—114no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4C22×D1111yescharacteristic
386C22×C4C22×D1111yescharacteristic
387C22×C4C22×D1111yescharacteristic
388C22×C4C22×D1111yescharacteristic
389C4⋊C4—222no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—41no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—222no—
403C42—222no—
404C11#243111yescharacteristic, complemented, Sylow
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—112no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23D4×D1112yes—
439C23D4×D1112yes—
440C23C23×D1111yescharacteristic
441Q8—228no—
442D4—28no—
443D4—44no—
444D4—44no—
445D4—228no—
446D4—228no—
447D4—444no—
448D4—444no—
449D4—444no—
450D4—444no—
451D4—444no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—112no—
463C2×C4—112no—
464C2×C4—112no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—112no—
468C2×C4—228no—
469C2×C4—228no—
470C2×C4—228no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4D4×D1112yes—
484C2×C4#434112yescomplemented
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—222no—
507C22—222no—
508C22—222no—
509C22—441no—
510C22—441no—
511C22—441no—
512C22—441no—
513C22—441no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—441no—
518C22—441no—
519C22—441no—
520C22C2×D4×D1111yescharacteristic
521C22C2×D4×D1111yescharacteristic
522C22C2×D4×D1111yescharacteristic
523C22C2×#434111yescharacteristic
524C22#6703711yescharacteristic
525C22#6703711yescharacteristic
526C22#41×D1111yescharacteristic
527C4—22no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—114no—
532C4—222no—
533C4—222no—
534C4—222no—
535C4—441no—
536C4—441no—
537C2—42no—
538C2—42no—
539C2—81no—
540C2—442no—
541C2—881no—
542C2D11×#12011yescharacteristic
543C2#1062312211yescharacteristic
544C2#1062312311yescharacteristic
545C2#1062312711yescharacteristic
546C2#1062313011yescharacteristic
547C2#1062314111yescharacteristic
548C2#1062324911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2431
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#4341C2semidirect
2. C2×#66993C2semidirect
3. C2×#66992C2semidirect
4. C2×#66938C2semidirect
5. C11×#392C2semidirect
6. #10622836C2semidirect
7. #10622836C2semidirect
8. #10622833C2semidirect
9. #10622573C2semidirect
10. #10622571C2semidirect
11. #10622570C2semidirect
12. #10622569C2semidirect
13. C22⋊C4×Dic11C2semidirect
14. #10622278C2semidirect
15. #10622259C2semidirect
92. C2×C22⋊D11D4semidirect
98. C22×Dic11D4semidirect
114. C2×Dic22D4semidirect
181. C2×C4×C11#41semidirect
207. C2×Dic11#41semidirect
218. #392D11semidirect
404. C11#2431semidirect
484. C2×C4#4341semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#43412
C2×#669932
C2×#669922
C2×#669382
C11×#3922
#106228362
#106228332
#106225732
#106225712
#106225702
#106225692
C22⋊C4×Dic112
#106222782
#106222592
#243111